Magnus Force Estimation using the principle of minimum pressure gradient

The flow around a rotating cylinder is one of the fundamental problems that piqued the interests of many venerable aerodynamicists and fluid mechanicians since the time of Lord Rayleigh. The force caused by the rotation of the cylinder has always been considered as an immediate consequence of viscosity, since the potential flow model failed entirely to predict the value of the circulation, due to the lack of a Kutta-like condition. On the other hand, Glauert modeled the flow outside the boundary layer of a rotating cylinder as a potential flow with an unknown circulation. He then obtained an approximate solution of Prandtl’s boundary layer equations and applied the no-slip condition to estimate the circulation in the outer flow. Interestingly, for rapidly rotating cylinders (α = ωR/U >> 1), up to fourth-order in the small parameter ϵ = 1/α, the obtained circulation is independent of viscosity. In this work, we use Glauert’s model of the outer flow over a rotating cylinder (i.e., a potential flow with an unknown circulation). However, instead of the tedious boundary layer calculations, we rely on the recently developed Principle of Minimum Pressure Gradient to obtain the unknown circulation. Perfect matching with Glauert’s solution is found. Moreover, our solution, in contrast to Glauerts’, points to the existence of different physics at small rotational speeds. The obtained results, given their perfect matching with Glauert’s solution (relying on the no-slip condition), points to a potential equivalence between the no-slip condition and fluid body forces.